What is the standard form of f(x)=x(x−2)2+4x−5?

1 Answer
Vikki
Mar 7, 2016

f(x)=x3−4x2+8x−1

Explanation:

The standard form of an polynomial function is written in descending order.

1) For this problem, we need to expand the function like this

f(x)=x(x−2)2+4x−5

f(x)=x(x−2)(x−2)+4x−5

2) Let's foil aka multiply and combine like terms

f(x)=x(x2−2x−2x+4)+4x−5
f(x)=x(x2−4x+4)+4x−5

3) Let's distribute x into the function to get

f(x)=x3−4x2+4x+4x−5

4) Now combine all like terms to get

f(x)=x3−4x2+8x−1

Now, our function is in the standard form.

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